WORD MATH PROBLEM

Question

The speed of the current in a river is 4 miles per hour. A boat travels 18 miles downstream (with the current) in this river in the same time that it travels 10 miles upstream (against the current). Find the speed of the boat in still water.

Answer 1

So, speed of the current is 4 mph.

 

When you travel downstream, your speed relative to the riverbank is the boat's speed relative tot the water PLUS the speed of the current. Vdown = Vboat + V river

 

When you travel upstream, your speed relative to the riverbank is the boat's speed relative to the water MINUS the speed of the current. Vup = Vboat - Vriver

 

The time to go downstream 18 miles is the same time to upstream 10 miles: call this 't'.

 

So, since distance = rate of travel times the time, 

 

18 miles = t * Vdown, and

10 miles = t * Vup.

 

Solve the first equation for t in terms of the other quantities.

Substitute for t in the second equation and solve for Vboat!